Bayesian analysis of the evidence for minor components in crystallographic models: an alternative to the Hamilton {\cal R} test

Abstract

A simple test based on Bayesian statistics for the presence of minority populations in single-crystal structure refinement is presented. The test is illustrated by analysis of photocrystallographic experiments on single crystals of ruthenium-sulfur-dioxide-based complexes. In data sets collected after irradiation with light, conventional refinements of the populations of different metastable states to values below 4% are shown to be statistically significant. The results also confirm that the photo-induced states are absent from data collected in the dark.

Quantifying Crystallographically Independent Optical Switching Dynamics in Ru SO2 Photoisomers via Lock-and-Key Crystalline Environment

“…Although a difference in the amount of disorder of the MS2 geometry was observed, an underlying η 1 -O-bound MS1 geometry was not crystallo- graphically resolved, and the differences in photoconversion and thermal stability between the different crystallographic centers were not examined. 11 This communication analyzes the reaction cavity through the examination of two members of the [Ru(NH 3 ) 4 SO 2 X]tosylate 2 family of complexes, X = isonicotinamide (1) and isonicotinic acid (2), both of which have two crystallographically distinct Ru centers. The reaction cavity is analyzed using two methods, Voronoi−Dirichlet polyhedra (VDP) partitioning, which quantifies the free volume around the photoisomerizable SO 2 , and Hirshfeld surfaces, which identifies the intermolecular interactions around the photoisomeriziable SO 2 .…”

“…In one complex, there was a single MS2 geometry at 26.9(10)% photoconversion; in the other complex, the MS2 geometry was disordered over three sites with a total photoconversion of 22.4(10)%. Although a difference in the amount of disorder of the MS2 geometry was observed, an underlying η 1 -O-bound MS1 geometry was not crystallographically resolved, and the differences in photoconversion and thermal stability between the different crystallographic centers were not examined …”

Overview of refinement procedures withinREFMAC5: utilizing data from different sources

“…Therefore, there will typically be many potential models that are consistent with the same set of observations. One approach intended to resolve this issue is the refinement of model ensembles (Burnley et al , 2012; Phillips & Cole, 2012; Hummer & Köfinger, 2016). Another approach is to use additional information (prior knowledge) to choose one model; the maximum a posterior probability (MAP) estimation method serves this purpose.…”